Álgebra Linear e Geometria Analítica

Theoretical (T) and theoretical-practical (TP) classes. The T classes take place in an essentially expository way, approaching the themes foreseen in the program, prevailing a strong interaction between the concepts and their concrete application. The TP classes will be aimed at solving problems and practical cases under the guidance of the teacher, carried out individually or in small groups.
Assessment: by exam for 20 points or by exam for 16 points plus 4-point Matlab project

The teaching of Mathematics should facilitate mathematical communication, reflective thinking, the application of mathematical techniques to problem solving, critical analysis of the results obtained, and finally, interdisciplinarity. One of the teaching objectives of Linear Algebra is to provide the basic foundations of mathematical methods, usually applied in the areas of Engineering.

1. Complex numbers
2. Systems of linear equations and matrices
2.1. Matrices
2.2. Special matrices
2.3. Operations with arrays and some properties
2.4. Invertible matrices
2.5. Characteristic of an array
2.6. Resolution of linear systems using the Gauss elimination method
2.7. Characteristic calculation using the Gaussian elimination method
2.8. Inverse matrix
2.9. Gauss-Jordan method
2.10. Application to Biomedical Engineering problems
3. Determinants
3.1. Determinants and their properties Sarrus Rule
3.2. Laplace’s theorem and its generalization
3.3. Gauss elimination method. Cramer’s Rule
4. Eigenvalues and eigenvectors
4.1. Value and eigenvector
4.2. Own spaces
4.3. Diagonalization of a matrix
4.4. Cayley-Hamilton theorem
5. Analytical Geometry
5.1. Outer and inner product of vectors
5.2. Line and plane equations
5.3. Intersection of lines and planes
5.4. Relative position between lines and planes
5.5. Angles between geometric identities

NAO